The determination of geoidal heights from astrogeodetic deflections of the vertical is limited in reliability by the lack of available data, and its generally poor distribution. In order to overcome this problem, one possible method is to use gravity data to assist in predicting deflections in areas where none have been, or can be, observed. This thesis investigates such a procedure, and evaluates the capabilities of a high order approximating polynomial to represent the geoid. The influence of the additional predicted deflections on the shape of the geoid is studied, and various alternatives for the determination of the detailed shapes of the geoid in a small area investigated. Satisfactory results have been obtained for deflection prediction. However, not all error sources have been accounted for, and further refinements, together with an improved gravity fields, will results in more reliable predictions. The use of the approximating polynomial has several advantages over the usual approach. Fewer deflection stations are needed than in the classical technique, and geoidal heights, together with their error covariance matrix, can be computed at any points in the region of interest. Geoidal heights, obtained from other sources, may be used as constraints on the solution. The techniques developed here should contribute significantly towards enabling deflections to be predicted at geodetic stations, and towards providing a reliable tool for geoid computation.
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